Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Hexahedron cell. More...

#include <Intrepid_HGRAD_HEX_C2_FEM.hpp>

Inheritance diagram for Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >:
Intrepid::Basis< Scalar, ArrayScalar >

List of all members.

Public Member Functions

 Basis_HGRAD_HEX_C2_FEM ()
 Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
 Evaluation of a FEM basis on a reference Hexahedron cell.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const
 FVD basis evaluation: invocation of this method throws an exception.

Private Member Functions

void initializeTags ()
 Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

Detailed Description

template<class Scalar, class ArrayScalar>
class Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Hexahedron cell.

Implements Lagrangian basis of degree 2 on the reference Hexahedron cell. The basis has cardinality 27 and spans a COMPLETE tri-quadratic polynomial space. Basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:

  =================================================================================================
  |         |           degree-of-freedom-tag table                    |                           |
  |   DoF   |----------------------------------------------------------|      DoF definition       |
  | ordinal |  subc dim    | subc ordinal | subc DoF ord |subc num DoF |                           |
  |=========|==============|==============|==============|=============|===========================|
  |    0    |       0      |       0      |       0      |      1      |   L_0(u) = u(-1,-1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1,-1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 1, 1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(-1, 1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    4    |       0      |       4      |       0      |      1      |   L_4(u) = u(-1,-1, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    5    |       0      |       5      |       0      |      1      |   L_5(u) = u( 1,-1, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    6    |       0      |       6      |       0      |      1      |   L_6(u) = u( 1, 1, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    7    |       0      |       7      |       0      |      1      |   L_7(u) = u(-1, 1, 1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    8    |       1      |       0      |       0      |      1      |   L_8(u) = u( 0,-1,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |    9    |       1      |       1      |       0      |      1      |   L_9(u) = u( 1, 0,-1)    |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   10    |       1      |       2      |       0      |      1      |   L_10(u) = u( 0, 1,-1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   11    |       1      |       3      |       0      |      1      |   L_11(u) = u(-1, 0,-1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   12    |       1      |       8      |       0      |      1      |   L_12(u) = u(-1,-1, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   13    |       1      |       9      |       0      |      1      |   L_13(u) = u( 1,-1, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   14    |       1      |      10      |       0      |      1      |   L_14(u) = u( 1, 1, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   15    |       1      |      11      |       0      |      1      |   L_15(u) = u(-1, 1, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   16    |       1      |       4      |       0      |      1      |   L_16(u) = u( 0,-1, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   17    |       1      |       5      |       0      |      1      |   L_17(u) = u( 1, 0, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   18    |       1      |       6      |       0      |      1      |   L_18(u) = u( 0, 1, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   19    |       1      |       7      |       0      |      1      |   L_19(u) = u(-1, 0, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   20    |       3      |       0      |       0      |      1      |   L_20(u) = u( 0, 0, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   21    |       2      |       4      |       0      |      1      |   L_21(u) = u( 0, 0,-1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   22    |       2      |       5      |       0      |      1      |   L_22(u) = u( 0, 0, 1)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   23    |       2      |       3      |       0      |      1      |   L_23(u) = u(-1, 0, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   24    |       2      |       1      |       0      |      1      |   L_24(u) = u( 1, 0, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   25    |       2      |       0      |       0      |      1      |   L_25(u) = u( 0,-1, 0)   |
  |---------|--------------|--------------|--------------|-------------|---------------------------|
  |   26    |       2      |       2      |       0      |      1      |   L_26(u) = u( 0, 1, 0)   |
  |=========|==============|==============|==============|=============|===========================|
  |   MAX   |  maxScDim=2  |  maxScOrd=12 |  maxDfOrd=0  |      -      |                           |
  |=========|==============|==============|==============|=============|===========================|
  
Remarks:
Ordering of DoFs follows the node order in Hexahedron<27> topology. Note that node order in this topology does not follow the natural oder of k-subcells where the nodes are located, except for nodes 0 to 7 which coincide with the vertices of the base Hexahedrn <8> topology. As a result, L_0 to L_7 are associated with nodes 0 to 7, but L_8 to L_19 are not associated with edges 0 to 12 in that order.

Definition at line 124 of file Intrepid_HGRAD_HEX_C2_FEM.hpp.


Member Function Documentation

template<class Scalar , class ArrayScalar >
void Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar &  outputValues,
const ArrayScalar &  inputPoints,
const EOperator  operatorType 
) const [inline, virtual]

Evaluation of a FEM basis on a reference Hexahedron cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Hexahedron cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods.

Parameters:
outputValues [out] - rank-2 or 3 array with the computed basis values
inputPoints [in] - rank-2 array with dimensions (P,D) containing reference points
operatorType [in] - operator applied to basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 104 of file Intrepid_HGRAD_HEX_C2_FEMDef.hpp.

References Intrepid::Basis< Scalar, ArrayScalar >::basisCardinality_, Intrepid::Basis< Scalar, ArrayScalar >::basisCellTopology_, Intrepid::Basis< Scalar, ArrayScalar >::getBaseCellTopology(), and Intrepid::Basis< Scalar, ArrayScalar >::getCardinality().


The documentation for this class was generated from the following files:

Generated on Tue Oct 20 15:10:08 2009 for Intrepid by  doxygen 1.6.1